1. Field of the Invention
The present invention is directed to a method and computed tomography apparatus for reconstructing an image from measured values acquired by conducting a spiral scan of an examination subject.
2. Description of the Prior Art
Methods are known for the reconstruction of images of a slice of an examination subject having a slice thickness with respect to an image plane from measured values acquired with a CT apparatus by conducting a spiral scan of the examination subject with an x-ray source rotating around the examination subject and a detector formed by at least one line of detector elements. In such known methods, measured values are respectively allocated to different projection angles .alpha. and to a z-position on the longitudinal axis of the spiral scan, and a constant, dimensionless pitch p is adhered to during the spiral scan. This pitch p is defined as the ratio of the relative longitudinal shift (in mm) between (a) the examination subject, the x-ray source and the detector which occurs per full revolution of the x-ray source around the examination subject, and (b) the longitudinal width (in mm) of a line of the detector. "Longitudinal" means the direction of the longitudinal axis of the spiral scan. CT apparatuses for the implementation of such methods are also known.
Methods and CT apparatuses of this type are disclosed in U.S. Pat. No. 5,559,847, European Application 0 713 678, U.S. Pat. No. 5,539,796 and in Polacin et al., "Evaluation of Section Sensitivity Profiles and Image Noise in Spiral CT", Radiology, 1992, No. 185, pages 29 through 35.
In the reconstruction of images from measured values acquired by spiral scanning with a CT apparatus having a single-line detector, an interpolation between the measured values lying in front of and behind the image plane is implemented for each projection angle for generating calculated projections in the desired image plane.
Two interpolation methods are currently most standard: In the first, a linear interpolation is undertaken between respectively two measured projections lying closest to the image plane, these having been registered at the same projection angle a but in different revolutions. This type of interpolation is referred as 360LI interpolation. In the second method, an interpolation also is undertaken between two projections lying closest to the image plane, but one is registered at the projection angle .alpha..sub.d and the other is registered at the projection angle .alpha..sub.c complementary thereto (.alpha..sub.c =.alpha..sub.d.+-..pi. is valid for the middle detector element of the detector). This type of interpolation is referred to as 180LI interpolation. Given the same pitch, it supplies narrower effective layer widths (characterized, for example, by the full width at half maximum FWHM of the layer sensitivity profile) than the 360LI interpolation. Given the same output power (mA value) of the x-ray source, for example an x-ray tube, the pixel noise is increased in comparison to the 360LI interpolation as a tradeoff. The artifact susceptibility is also higher. Both interpolation types are illustrated schematically in FIG. 2 for the pitch p=2, with the projection angle .alpha. being shown as a function of the detector position in the z-direction. The projection angle .alpha. is entered on the longitudinal axis of the spiral scan (z-position) relative to the position normalized to the width b of a line of the detector.
All conventional interpolation methods for spiral scanning with a single-line detector have in common the fact that the width of the slice sensitivity profile (characterized, for example, by the full width at half maximum FWHM) increases with increasing pitch p. This is shown in FIG. 3 for the 180LI and the 360LI interpolation, which shows the full width at half maximum FWHM of the slice sensitivity profile referred to the collimated layer thickness d.sub.coll as a function of the pitch p. The relationship according to FIG. 3 complicates the procedure, particularly for unfamiliar users and represents a limitation in the selection of the examination parameters.
The situation becomes even less easily predictable when conventional interpolation techniques, for example the 36OLI or 180LI interpolation, are employed for spiral scans implemented with a multi-line detector. FIG. 4 shows the full wave at half maximum FWHM of the slice sensitivity profile deriving in a 360LI and in a 180LI interpolation, again relative to the collimated slice thickness d.sub.coll, as a function of the pitch p for a CT apparatus having a five-line detector. The full wave at half maximum now changes non-monotonously with the pitch. The relationship is not intuitive and is difficult to understand. Thus, for example, the full wave at half maximum FWHM can decrease given increasing pitch p.